September 2016 Page 9 of 34
College- and Career-Readiness Standards for Mathematics
Expressions and Equations
Analyze and solve linear equations and pairs of simultaneous linear equations
8.EE.7a
Solve linear equations in one
variable.
a. Give examples of linear
equations in one variable with
one solution, infinitely many
solutions, or no solutions.
Show which of these
possibilities is the case by
successively transforming
the given equation into
simpler forms, until an
equivalent equation of the
form x = a, a = a, or a = b
results (where a and b are
different numbers).
Desired Student Performance
• The product of a number and its
multiplicative inverse is 1.
×
= 1,
where a 0 and b 0.
• The coefficient is the numerical
factor of a term that contains a
variable.
• An equation is a sentence stating
that two quantities are equal.
• The solution of an equation is the
value of a variable that makes the
equation true.
• Addition property of equality.
• Subtraction property of equality
• Multiplication property of equality.
• Division property of equality.
• A two-step equation contains two
operations.
• How to solve simple one-step
equations.
A student should understand
• How to find the multiplicative inverse of
a number.
• To solve an equation in which the
coefficient is not 1, you must multiply or
divide each side by the coefficient of
the variable. For example, in the
equation -3x = 12, you must divide both
sides by -3. A common error in
problems of this type is for students to
divide both sides by 3.
• Some equations have variables on
each side of the equals sign. To solve,
use the properties of equality to write
an equivalent equation with the
variables on one side of the equal sign
and then solve the equation.
• Some equations have no solution.
When this occurs, the solution is the
null set or empty set and is shown by
the symbol or { }. After solving the
equation, the solution will look like a =
b, where a and b are different numbers.
• Other equations may have every
number as their solution. An equation
that is true for every value of the
variable is called an identity. After
solving the equation, the solution will
look like a = a.
A student should be able to do
.
• Solve an equation using the
multiplicative inverse.
• Solve an equation using the
addition, subtraction, multiplication,
or division properties of equality to
justify the steps to the solution.
• Solve multistep equations in which
coefficients and constants may be
any rational number.
• Translate a word phrase or real-
world problem into an equation.
• Solve equations with variables on
both sides of the equal sign.
• Determine if an equation has no
solution.
• Determine if an equation is an
identity with infinitely many
solutions.
• Create equations that have one
solution, infinitely many solutions,
or no solution.
• Classify equations by the number
of solutions.